The intention of the Bulletin17B low outlier censoring threshold is to obtain better correspondence between the top plotting position in the gage record and the estimated lpiii distribution. The purpose of this section is to examine if this low outlier censoring threshold developed for peak annual flows is relevant for volume duration frequency curves. Note that this analysis was originally performed for the Iowa River regulated flow frequency study and the following is taken from the report describing that study (Corps of Engineers, 2009).
The Bulletin 17B low outlier censoring is intended to prevent small frequent flows for having undue influence on the estimates of large, infrequent flows. This is a particular problem when using logarithms of flows with sample standard moments to estimate a frequency distribution. The problem can be seen by considering two observed flows of magnitude 10 and 1000. The log10 values for these two values are 1
and 3, reducing the difference considerably. This reduced difference gives the smaller values much more influence in the computation of the standard deviation, which is proportional to the squared differences with the mean, and the skew, which is proportional to the cubed difference with the mean.
The difficulty of course, is determining the appropriate threshold flow below which low-values should be censored. Thomas (1985, pg.330) describes how this threshold was established by the Bulletin17B work group members:
The first step in the analysis of the outlier tests was to apply the outlier test to observed peak discharge data for 50 gaging stations for low outlier detection only. All work group members subjectively identified the number of outliers for each station. On the basis of the number of low outliers identified by each test as compared to the consensus of the work group, 50 outlier test were reduced to 10 tests to detect high outliers as well and apply the test to simulated log-
Pearson Type III data. ….The 10 outlier tests were applied to simulated samples and the sample estimates of the 2, 10 and 100 year flood discharges were compared to the true values. On the basis of the bias and root mean square of the 2-, 10- and 100 year flood discharges, the 10 tests were reduced to 6. On the basis of the number of outliers identified by each test as compared to the consensus of the work group, the Grubbs and Beck tests using either zero skew or generalized at a 10% level of significance gave the most reasonable results.
The Bulletin 17B work group decided to use the zero skew approach because it would not be affected by the various estimates of regional (generalized) skew available from skew maps and zero skew was consistent with the development of the Grubbs and Beck statistic.
Reapplying the entire Bulletin 17B work group procedure for identifying a low-outlier criterion is beyond the scope of this study. Instead, a page will be taken out of the group’s procedure by examining the performance of low-outlier censoring threshold for a large group of gages, this time located in Iowa. The focus will be on the bias of lpiii estimates in comparison to the top plotting position in the flow period of record. Invariably, the 1993 or 2008 events are the top ranking floods for all flow durations greater than 1day.
Three different low-outlier censoring levels used were:
The Bulletin 17B low outlier threshold determined by the Grubbs and Beck statistic at a 10% significance level;
Censoring at the 0.70 exceedance probability; Censoring at the 0.57 exceedance probability
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The 0.57 exceedance probability was used to approximate channel capacity while still ensuring enough data points to be able to apply the Bulletin 17B conditional probability adjustment formulas.Practically speaking, the Bulletin 17B low outlier censoring level does results in a small number of values being censored in the period of record, perhaps one or two (see Tables 6.1 and 6.2). Censoring a few relatively small values is important in that it does not reduce significantly the number of flow magnitudes to estimate flow frequency curve statistics. Note, that censoring does not reduce the effective record length (see discussion of conditional probability adjustment used in the low-outlier analysis in Bulletin 17B, IACWD, 1982, Appendix 5). However, the flow magnitude of the censored values is not used in computing distribution statistics.
The Bulletin 17B work group did not investigate the affect on prediction accuracy of censoring flows by performing a split sample investigation as described in Bulletin 17B (IACWD, 1982, appendix 14). This is not likely to affect prediction accuracy because of the few number of values censored using the
Bulletin17B threshold. However, a threshold based on the 0.7 or 0.57 exceedance probability will censor up to almost half the period of record. This has a much larger influence on the information available to estimate flow frequency curve statistics. In the Upper Mississippi Study (Corps of Engineers, 2000, Sections 4 and 5), flow frequency curve distribution/estimation pairings were compared in split sample studies. Pairings using full data sets almost uniformly out performed methods censoring the data below the median (50% exceedance probability). The censored methods used the log-Normal and Gumbel distributions, not the lpiii. Consequently, some caution needs to be used in interpreting the relative value of censoring thresholds because of the potential loss of prediction accuracy as the number of censored values increases. There is a trade-off between censoring values to obtain a better correspondence between the flow frequency distribution and the top plotting position and the potential reduction in prediction accuracy obtained from not using censored flow magnitudes to estimate distribution statistics. The low outlier censoring tests were applied to the Iowa and Des Moines River gages discussed in the previous section, the Iowa gages described in Table 6.1 and the very large area gages used in the Upper Mississippi study described in Table 6.2.
The comparisons between censoring thresholds was made by computing the average over all gages of the fraction difference between the top plotting position and the lpiii distribution prediction as a measure of bias. The fraction difference is computed as:
fraction difference = (lpiii flow prediction – top plotting position flow)/top plotting position flow
The average fraction difference computed for the Iowa Gages (Table 6.1) resulted in little difference between methods as is shown in Table 6.3. The Bulletin17B threshold was best for the 15day and 30day annual maximum flows, and, the censoring threshold was best for the remaining durations. The range in error was not a function of record length as can be seen from Figure 6.1 for the 1day duration, which is typical of all the other durations. What is interesting from this plot is how the range in error decreases for the exceedance probability thresholds which censor more flows.
The average fraction differences computed for the Iowa gages were compared to Iowa and Des Moines River gages used in this study and the Upper Mississippi River gages in Tables 6.4 and 6.5 for the 1day and 30day duration annual maximum volumes. The difference between the average fractional estimates are typical for other durations. Unlike the Iowa gage comparisons, the exceedance probability thresholds perform somewhat better than the Bulletin17B threshold values. Interestingly, the 0.7 exceedance probability threshold performs somewhat better than the 0.57 exceedance probability for the Iowa and Des Moines River gages.
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The average bias does not provide a complete picture of the value of a particular censoring threshold. The distribution of fraction difference shown in Figures 6.2-6.4 for the 1day duration and Figures 6.5-6.7 for the 30day duration reveal that the Bulletin17B threshold provides a more symmetrical distribution about zero difference than the other methods, but a much greater range of errors for the Iowa gages. Conclusion regarding the other gages is more difficult. The same trend in the symmetry of errors about zero seems to be apparent as with the Iowa gages for the different censoring thresholds; but the difference in range between thresholds is more difficult to discern for the Iowa and Des Moines Rivers. Evaluation of the errors for the Iowa and Des Moines River, and, the Mississippi gages is certainly hampered by the small number of gages.In conclusion, the improvement obtained by increasing the number values censored is not apparent based on the average fraction difference alone. This is particularly true for the large number of Iowa gages available. The advantage of censoring more values comes from the reduction in the range of fractional difference about zero difference.
There is no doubt that censoring more values results in greater correspondence between the top plotting position and the lpiii flow frequency curve predictions. See for example the comparisons shown in Figures 6.8-6.11 comparing plotting positions and lpiii 30day and 120day frequency curve for different censoring thresholds at Coralville Reservoir and Wapello on the Iowa River. The correspondence of plotting position and lpiii prediction is superior when more flows are censored than indicated by the Bulletin17B threshold.
So what censoring level should be selected? Improved accuracy cannot be used as an argument since no split sample testing was performed. The arguments in favor of the Bulletin 17B threshold are that:
it is the regulatory method;
it performs as well as the other threshold methods in terms of fractional difference;
the distribution of differences about zero difference is more symmetrical than the other threshold methods;
lpiii frequency curve statistics are estimated from more flows, potential resulting in greater prediction accuracy.
The arguments in favor of using a greater censoring level than Bulletin 17B:
the average fractional difference is comparable to the error obtained from the Bulletin 17B threshold;
the range in fractional difference is considerably smaller than that from the Bulletin 17B threshold;
the correspondence between the lpiii predictions and top plotting position for the Iowa; and Des Moines River is better than when using the Bulletin 17B threshold;
Basically, the analysis of all the gages does not present enough evidence to deviate from the regulatory method. Selecting an alternative to Bulletin 17B based on a comparison with only the Iowa River and Des Moines River gages would not be appropriate because of limited number of gages and the potential for large sampling error.
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Table 6.1: Additional Iowa Gages Used in Low Censoring AnalysisUSGS Gage Description Area Years
5412500 Turkey River at Garber, IA 1545 37
5418500 Maquoketa River near Maquoketa, IA 1553 41
5420560 Wapsipinicon River near Elma, IA 95.2 15
5422000 Wapsipinicon River near De Witt, IA 2336 35
5422470 Crow Creek at Bettendorf, IA 17.8 12
5449000 East Branch Iowa River near Klemme, IA 133 15
5449500 Iowa River near Rowan, IA 429 31
5451500 Iowa River at Marshalltown, IA 1532 37
5451700 Timber Creek near Marshalltown, IA 118 25
5451900 Richland Creek near Haven, IA 56.1 26
5452000 Salt Creek near Elberon, IA 201 25
5452200 Walnut Creek near Hartwick, IA 70.9 23
5453000 Big Bear Creek at Ladora, IA 189 27
5453100 Iowa River at Marengo, IA 2794 22
5454300 Clear Creek near Coralville, IA 98.1 25
5455500 English River at Kalona, IA 574 29
5457700 Cedar River at Charles City, IA 1054 15
5458000 Little Cedar River near Ionia, IA 306 23
5458500 Cedar River at Janesville, IA 1661 34
5458900 West Fork Cedar River at Finchford, IA 846 25
5459500 Winnebago River at Mason City, IA 526 36
5462000 Shell Rock River at Shell Rock, IA 1746 22
5463000 Beaver Creek at New Hartford, IA 347 28
5463500 Black Hawk Creek at Hudson, IA 303 20
5464000 Cedar River at Waterloo, IA 5146 27
5464500 Cedar River at Cedar Rapids, IA 6510 44
5470000 South Skunk River near Ames, IA 315 34
5470500 Squaw Creek at Ames, IA 204 20
5471000 South Skunk River below Squaw Creek near Ames, IA 556 21
5471200 Indian Creek near Mingo, IA 276 18
5471500 South Skunk River near Oskaloosa, IA 1635 29
5472500 North Skunk River near Sigourney, IA 730 26
5473400 Cedar Creek near Oakland Mills, IA 530 10
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Table 6.1: Additional Iowa Gages Used in Low Censoring Analysis (continued)USGS Gage Description Area Years
5476500 Des Moines River at Estherville, IA 1372 22
5479000 East Fork Des Moines River at Dakota City, IA 1308 29
5480500 Des Moines River at Fort Dodge, IA 4190 33
5481000 Boone River near Webster City, IA 844 33
5481950 Beaver Creek near Grimes, IA 358 21
5482300 North Raccoon River near Sac City, IA 700 18
5482500 North Raccoon River near Jefferson, IA 1619 28
5483450 Middle Raccoon River near Bayard, IA 375 12
5484000 South Raccoon River at Redfield, IA 994 28
5484500 Raccoon River at Van Meter, IA 3441 42
5484800 Walnut Creek at Des Moines, IA 78.4 17
5485640 Fourmile Creek at Des Moines, IA 92.7 17
5486000 North River near Norwalk, IA 349 27
5486490 Middle River near Indianola, IA 489.4 28
5487470 South River near Ackworth, IA 460 26
5487980 White Breast Creek near Dallas, IA 333 21
5489000 Cedar Creek near Bussey, IA 374 28
5494300 Fox River at Bloomfield, IA 87.7 11
6483500 Rock River near Rock Valley, IA 1592 25
6485500 Big Sioux River at Akron, IA 8424 33
6602400 Monona-Harrison Ditch near Turin, IA 900 29
6605000 Ocheyedan River near Spencer, IA 426 13
6605850 Little Sioux River at Linn Grove, IA 1548 14
6606600 Little Sioux River at Correctionville, IA 2500 37
6607200 Maple River at Mapleton, IA 669 31
6607500 Little Sioux River near Turin, IA 3526 32
6608500 Soldier River at Pisgah, IA 407 27
6609500 Boyer River at Logan, IA 871 33
6807410 West Nishnabotna River at Hancock, IA 609 22
6808500 West Nishnabotna River at Randolph, IA 1326 27
6809210 East Nishnabotna River near Atlantic, IA 436 20
6809500 East Nishnabotna River at Red Oak, IA 894 32
6810000 Nishnabotna River above Hamburg, IA 2806 31
6898000 Thompson River at Davis City, IA 701 36
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Table 6.2 Upper Mississippi GagesLocation Area Years
Winona 36800 80 Saint Paul 59200 110 Dubuque 82000 71 Clinton 85600 111 Keokuk 119000 100 Hannibal 137000 100
Table 6.3: Comparison of Average fraction bias for Low Outlier Censoring Methods for all USGS gages1 average maximum minimum censoring 2Bulletin 17B 3p0.7 4p0.57 Bulletin 17B p0.7 p0.57 Bulletin 17B p0.7 p0.57 1day -0.031 0.042 -0.026 0.438 0.249 0.003 -0.406 -0.246 -0.101 15day -0.014 0.043 -0.021 0.378 0.342 0.018 -0.352 -0.163 -0.092 30 day -0.017 0.034 -0.021 0.374 0.414 0.024 -0.310 -0.213 -0.074 60 day -0.034 0.030 -0.021 0.284 0.499 0.014 -0.331 -0.149 -0.080 90 day -0.045 0.033 -0.021 0.259 0.515 0.013 -0.320 -0.178 -0.088 105 day -0.045 0.033 -0.021 0.259 0.515 0.013 -0.320 -0.178 -0.088 120day -0.059 0.029 -0.020 0.309 0.535 0.014 -0.361 -0.183 -0.095 1
Fraction bias = (lpiii distribution estimated flow – top plotting position)/top plotting position 2
Bulletin 17B low outlier threshold, 3censor below 0.7 exceedance probability,4 censor below 0.57 exceedance
probability
Table 6.4: Comparison of Average fraction bias for Low Outlier Censoring Methods 1day duration: USGS, Iowa and Des Moines River and Upper Mississippi River1
average maximum minimum
censoring 2 Bulletin 17B 3p0.7 4p0.57 Bulletin 17B p0.7 p0.57 Bulletin 17B p0.7 p0.57 usgs -0.031 0.042 -0.026 0.438 0.249 0.003 -0.406 - 0.246 - 0.101 I&D4 -0.058 0.020 -0.011 0.154 0.118 0.074 -0.266 - 0.167 - 0.187 Mississippi -0.076 0.047 -0.006 -0.018 0.149 0.007 -0.115 0.005 - 0.014 1
Fraction bias = (lpiii distribution estimated flow – top plotting position)/top plotting position 2
Bulletin 17B low outlier threshold, 3censor below 0.7 exceedance probability, 4censor below 0.57 exceedance
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Table 6.5: Comparison of Average fraction bias for Low Outlier Censoring Methods30day duration: USGS, Iowa and Des Moines River and Upper Mississippi River1
average maximum minimum
censoring Bulletin 17B 3p0.7 4p0.57 Bulletin 17B p0.7 p0.57 Bulletin 17B p0.7 p0.57 usgs -0.017 0.034 -0.021 0.374 0.414 0.024 -0.310 -0.213 -0.074 I&D4 -0.093 -0.009 -0.051 -0.015 0.052 0.026 -0.199 -0.050 -0.099 Mississippi -0.091 0.040 -0.002 -0.010 0.088 0.006 -0.205 -0.011 -0.011 1
Fraction bias = (lpiii distribution estimated flow – top plotting position)/top plotting position 2
Bulletin 17B low outlier threshold, 3censor below 0.7 exceedance probability, 4censor below 0.57 exceedance
probability, 4Iowa and Des Moines River Gages
FIGURE 6.1: USGS GAGES FRACTION BIAS FOR BULLETIN 17B CENSORING THRESHOLD (censoring threshold equal to 0.7 exceedance probability (prob0.7),
censoring threshold equal to exceedance probability 0.57
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FIGURE 6.2: ALL GAGE 1DAY DURATION FRACTION BIAS COMPARISON
(censoring threshold 0.57 exceedance probability, iprob0.57 – Iowa and Des Moines River gages, prob0.57 – USGS gages, mprob0.57 – Mississippi River gages)
FIGURE 6.3: ALL GAGE 1DAY DURATION FRACTION BIAS COMPARISON
(censoring threshold 0.7 exceedance probability, iprob0. 7 – Iowa and Des Moines River gages, prob0. 7 – USGS gages, mprob0. 7 – Mississippi River gages)
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FIGURE 6.4: ALL GAGE 1DAY DURATION FRACTION BIAS COMPARISON
(Bulletin 17B censoring threshold Bulletin 17B. iBulletin 17B – Iowa and Des Moines River gages, mBulletin 17B – USGS gages)
FIGURE 6.5: ALL GAGE 30DAY DURATION FRACTION BIAS COMPARISON
(censoring threshold 0.57 exceedance probability, iprob0.57 – Iowa and Des Moines River gages, prob0.57 – USGS gages, mprob0.57 – Mississippi River gages)
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FIGURE 6.6: ALL GAGE 30DAY DURATION FRACTION BIAS COMPARISON (censoring threshold 0.7 exceedance probability, iprob0. 7 – Iowa and Des Moines River gages, prob0. 7 – USGS gages, mprob0. 7 – Mississippi River gages) FIGURE 6.7: ALL GAGE 30DAY DURATION FRACTION BIAS COMPARISONBulletin 17B censoring threshold Bulletin 17B. iBulletin 17B – Iowa and Des Moines River gages, mBulletin 17B – USGS gages
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FIGURE 6.8: CORALVILLE RESERVOIR COMPARISON LPIII DISTRIBUTION AND PLOTTING POSITIONS, 30DAYANNUAL MAXIMUM INFLOW FREQUENCY CURVE
thresh1 – Bulletin 17B censoring, thresh2 – censor at 0.7 exceedance probability, thresh3 – censor at 0.57 exceedance probability
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FIGURE 6.9: CORALVILLE RESERVOIR COMPARISON LPIII DISTRIBUTION AND PLOTTING POSITIONS, 120DAYANNUAL MAXIMUM INFLOW FREQUENCY CURVE
thresh1 – Bulletin 17B censoring, thresh2 – censor at 0.7 exceedance probability, thresh3 – censor at 0.57 exceedance probability
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FIGURE 6.10: WAPELLO COMPARISON LPIII DISTRIBUTION AND PLOTTING POSITIONS, 30DAY ANNUAL MAXIMUM FLOW FREQUENCY CURVE thresh1 – Bulletin 17B censoring, thresh2 – censor at 0.7 exceedance probability, thresh3 – censor at 0.57 exceedance probability52
FIGURE 6.11: WAPELLO COMPARISON LPIII DISTRIBUTION AND PLOTTING POSITIONS120day annual maximum flow frequency curve, thresh1 – Bulletin 17B censoring, thresh2 – censor at 0.7 exceedance probability, thresh3 – censor at 0.57 exceedance probability